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Techniques of optimal control are applied to a blood circulation model of cardiopulmonary resuscitation (CPR), which is described by a nonlinear system of seven difference equations. The variables are the pressures in the seven components of the model, namely: abdominal aorta, inferior vena cava, carotid arteries, jugular veins, thoracic aorta, right heart and superior vena cava, and thoracic pump (pulmonary vasculature and left heart). Forcing terms, representing chest and abdominal pressures, act as controls. The controls at two previous time steps give input to the seven pressure components at the current time step, which is a novel feature from the control viewpoint. We seek to maximize the blood flow, as measured by the systemic perfusion pressure, i.e., the pressure difference between the thoracic aorta and the right heart, summed over all the time steps. In principle, an increase in the blood flow would result in an increase of the surviving rates of the CPR procedure. By applying optimal control methods, we characterize the optimal waveforms for external chest and abdominal compression/decompression in terms of the original model coupled with corresponding adjoint equations. Numerical results for several scenarios are given, calculated using an iterative method. The optimal waveforms confirm the positive effects of active decompression and interposed abdominal compression.

Presents an approach to designing smart monitoring and control devices based on linearization of the system obtained from factoring the discrete system covariance matrix. The methods are nonparametric which allows the smart devices to operate with only a low level logic. >

The authors consider a problem of controlling the solution of the heat equation with the convective boundary condition, taking the heat transfer coefficient as a control parameter. The existence and uniqueness of the solution of the optimality system are established, and thus the unique optimal control is determined in terms of the solution of the optimality system. >

A system of two stationary semilinear elliptic partial differential equations (PDEs) with rather general competitive interactions is considered. The motivation is related to possible applications of the formalism to competitive/conflict situations and, in particular, to classical warfare for which systems of this type have been applied with rather promising results. The optimal strategies, mathematically defined in terms of minimizing or maximizing a certain function, are realized by varying the control functions. The authors show that a unique saddle point exists and is represented by the solution of the optimality system. The optimality system consists of two elliptic PDE state equations coupled with two adjoint equations. >

This paper concerns the optimal stopping time problem for a piecewise deterministic process. The associated dynamic programming equation is a variational inequality with integral and first order differential terms Our main results are W1,?-existence results and probabilistic representations for the solutions of these variational inequalities in bounded domains and in IRn.

Existence and regularity results are obtained for Bellman equation with integro-differential operators, corresponding to the stochastic control of diffusion processes with jumps.

We study the problem of optimal control of a deterministic system with final state constraints using dynamic programming methods. We present a penalization scheme and regularity results for the optimal cost function.

We consider switching games for piecewise-deterministic processes and the associated system of integro-differential equations. The viscosity solution of the system on Rn is a saddle point for the game.

We study the problems of optimal switching control of diffusion processes with additional obstacles and switching control of random evolutions.